We test a recently proposed wall-crossing formula for the change of the Hilbert space of BPS states in d = 4, N = 2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wall-crossing formula reproduces results of Göttsche and Yoshioka on wall-crossing behavior of the moduli of slope-stable holomorphic bundles over holomorphic surfaces. Our comparison shows very clearly that the moduli space of the D4D2D0 system on a rigid surface in a Calabi-Yau is not… CONTINUE READING